134 lines
4.6 KiB
Python
134 lines
4.6 KiB
Python
from loong import *
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import json
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import numpy as np
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import sys
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import matplotlib.pyplot as plt
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class GoodOrbit(Orbit):
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def __init__(self):
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self.kAlpha = mp.mpf("1.7") / (2 * mp.pi)
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self.kCriticalTheta = 2.86 / ((2 / 3) * self.kAlpha)
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self.r = (1 / 3) * self.kAlpha * mp.sqrt(1 + self.kCriticalTheta**2)
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self.point_A_cartesian = (
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self.kAlpha * self.kCriticalTheta * mp.cos(self.kCriticalTheta),
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self.kAlpha * self.kCriticalTheta * mp.sin(self.kCriticalTheta),
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)
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self.point_B_cartesian = (-self.kAlpha * self.kCriticalTheta * mp.cos(self.kCriticalTheta),
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-self.kAlpha * self.kCriticalTheta * mp.sin(self.kCriticalTheta))
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self.kPhi = mp.atan(self.kCriticalTheta)
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dx, dy = self.point_A_cartesian[0] - self.point_B_cartesian[0], self.point_A_cartesian[1] - self.point_B_cartesian[1]
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self.angle = mp.atan2(dy, dx)
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self.point_C1_cartesian = (self.point_A_cartesian[0] - 2 * self.r * dx, self.point_A_cartesian[1] - 2 * self.r * dy)
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self.point_C2_cartesian = (self.point_B_cartesian[0] + 1 * self.r * dx, self.point_B_cartesian[1] + 1 * self.r * dy)
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self.radius_of_C1 = 2 * self.r
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self.radius_of_C2 = 1 * self.r
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self.arclength = 6 * self.r * self.kPhi
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self.edge_k = self.kAlpha * mp.sqrt(1 + self.kCriticalTheta * self.kCriticalTheta)
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self.n = -1
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for i in range(3, 20, 2):
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self.a = (self.arclength - 2 * self.edge_k * self.kCriticalTheta) / (2 * (1 - i) * self.kCriticalTheta**i)
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self.b = (i * self.arclength - 2 * self.edge_k * self.kCriticalTheta) / (2 * (i - 1) * self.kCriticalTheta)
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if self.a > 0 and self.b > 0:
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self.n = i
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break
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print(f"arclength={self.arclength}", file=sys.stderr)
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print(f"edge_k={self.edge_k}", file=sys.stderr)
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print(f"a={self.a}", file=sys.stderr)
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print(f"b={self.b}", file=sys.stderr)
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print(f"n={self.n}", file=sys.stderr)
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print(f"now k={self.n*self.a*self.kCriticalTheta**(self.n-1)+self.b}", file=sys.stderr)
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if self.n == -1:
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raise Exception("n must be set")
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self.edge_raw_C = self.kAlpha * 0.5 * (
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self.kCriticalTheta * mp.sqrt(1 + self.kCriticalTheta * self.kCriticalTheta) -
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mp.log(-self.kCriticalTheta + mp.sqrt(1 + self.kCriticalTheta * self.kCriticalTheta)))
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def InitIdx(self):
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return mp.mpf("0.0")
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def InitC(self):
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return mp.mpf("0.0")
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def Idx2C(self, idx): # this function must be monotonically increasing
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if idx >= 0:
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theta = idx + self.kCriticalTheta
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tmp = mp.sqrt(1 + theta * theta)
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return self.kAlpha * 0.5 * (theta * tmp - mp.log(-theta + tmp)) - self.edge_raw_C
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elif idx >= -2 * self.kCriticalTheta:
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x = idx + self.kCriticalTheta
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y = (self.a * (x**self.n) + self.b * x) - 0.5 * self.arclength
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return y
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else:
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theta = -idx - self.kCriticalTheta
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tmp = mp.sqrt(1 + theta * theta)
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return -self.kAlpha * 0.5 * (theta * tmp - mp.log(-theta + tmp)) + self.edge_raw_C - self.arclength
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def Idx2Cartesian(self, idx):
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return mp.matrix([mp.cos(idx), mp.sin(idx)])
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def C2Idx(self, C):
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def f(idx):
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return self.Idx2C(idx) - C
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return mp.findroot(f, 0, solver='secant')
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def GenerateNextPointIdx(self, cur_point_idx, expected_distance):
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return cur_point_idx + expected_distance
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orbit = GoodOrbit()
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def f(x):
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return float(orbit.Idx2C(x))
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# 获取 kCriticalTheta
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kCriticalTheta = float(orbit.kCriticalTheta)
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print(f"kCriticalTheta={kCriticalTheta}")
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# 定义范围 [-kCriticalTheta-1, kCriticalTheta +1]
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start = -2.5 * kCriticalTheta - 1
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end = 0.5 * kCriticalTheta + 1
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# 生成范围内的点
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x_vals = np.linspace(start, end, 1000)
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# 计算 f(x) 的值
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y_vals = [f(mp.mpf(x)) for x in x_vals]
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# 绘制图像
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plt.figure(figsize=(10, 6))
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plt.plot(x_vals, y_vals, label='Idx2C(x)')
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plt.title('Idx2C function plot')
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plt.xlabel('Index (x)')
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plt.ylabel('C Value')
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plt.grid(True)
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plt.axhline(0, color='black', linewidth=0.5)
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plt.axvline(0, color='black', linewidth=0.5)
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plt.legend()
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plt.show()
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sys.exit()
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if __name__ == "__main__":
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orbit = GoodOrbit()
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loong = Loong(orbit, 224, mp.mpf("2.0"), mp.mpf("1e-8"))
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res_list = []
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for ti in range(-100, 101):
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print(f"calculating time_point={ti}")
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res_list.append(loong.CalcStatusListByTime(mp.mpf(ti)))
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# 转换成内置浮点数并保留6位
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float_res_list = [[{
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"idx": round(float(node["idx"]), 6),
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"node": [
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round(float(node["node"][0]), 6),
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round(float(node["node"][1]), 6),
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],
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"C": round(float(node["C"]), 6),
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"v": round(float(node["v"]), 6),
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} for node in res] for res in res_list]
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with open("A4_res.json", "w") as file:
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json.dump(float_res_list, file, indent=4)
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